Impact of natural enemies on obligately cooperative breeders

Obligately cooperative breeders (cooperators) display a negative growth rate once they fall below a minimum density. Constraints imposed by natural enemies, such as predators or competitors, may push cooperator groups closer to this threshold, thus increasing the risk that stochastic fluctuations will drive them below it. This may indirectly drive these groups to extinction, thereby increasing the risk of population extinction. In this paper, we construct mathematical models of the dynamics of groups of cooperators and non-cooperators in the presence of two types of enemies: enemies whose dynamics do not depend on the dynamics of their victim (e.g., amensal competitor, generalist predator) and those whose dynamics do. In the latter case, we distinguish positive (e.g., specialist predator) and negative (e.g., bilateral competitor) reciprocal effects. These models correspond to the classical amensal, predation and competition models, in the presence of an Ailee effect. We then develop the models to study consequences at the population level. By comparing models with or without an Allee effect, we show that enemies decrease the group size of cooperators more than that of non-cooperators, and this increases their group extinction risk. We also demonstrate how an Allee effect at a lower dynamical level call have consequences at a higher level: inverse density dependence at the group level generated lower population sizes and higher risks of population extinction. Our results also suggest that demographic compensation can be achieved by cooperators through an increased intrinsic growth rate, or by decreasing the enemy constraint. Both of these types of compensation have been observed in empirical studies of cooperators.